(15:16) Why does Paul refer to himself as a “priest,” when the book of Hebrews does away with the OT priestly system?
Paul is lifting OT imagery to explain a NT practice. In the OT, priests would offer a thanks offering to God for his covenant and his love. Here, Paul says that his work of evangelism in reaching the Gentiles is the thanks offering.
(Phil. 2:17 NASB) But even if I am being poured out as a drink offering upon the sacrifice and service of your faith, I rejoice and share my joy with you all.
(Rom. 15:19 NLT) They were convinced by the power of miraculous signs and wonders and by the power of God’s Spirit. In this way, I have fully presented the Good News of Christ from Jerusalem all the way to Illyricum.
Craig Blomberg: “Illyricum was a territory on the eastern shore of the Adriatic Sea that overlapped parts of what today would be Albania and Macedonia. From Illyricum to Jerusalem marks out roughly the eastern, Greek-speaking half of the Roman Empire in Paul’s day, or at least its most densely populated parts.”
 Blomberg, Craig. From Pentecost to Patmos: an Introduction to Acts through Revelation. Nashville, TN: B & H Academic, 2006. 233.